Individual and collective dynamics of contact behaviour
Sebastian Funk
18 May, 2017
SIMID Workshop
Questions
- What is the relative importance of individual vs collective variation in contact behaviour?
- How can we find out about long-term changes in collective contact behaviour
Individual vs. collective variation in contact behaviour
Longitudinal contact data
- There is variation in the number of contacts both within and between individuals
- The number of contacts is overdispersed both on the individual and the collective scales
Are there high-contact individuals or high-contact days?
- Hierarchical model implemented in stan
- Negative binomial model with two parameters vs negative binomial with two parameters per person, compared with Deviance Information Criterion (DIC)
Model comparison
\(\mathrm{contacts} \sim \mathrm{NegBin(\mu, k)}\)
| Model | Δ DIC |
|---|---|
| Collective | 0 |
| Individual | -5k |
Covariates
Age
Age
Household size
Urban/rural
Covariate model
\(\mathrm{contacts} \sim \mathrm{NegBin(\mu, k)}\)
\(\log(\mu) = \alpha + \beta_\mathrm{a} \cdot \mathrm{age} + \ldots\)
Model comparison
\(\mathrm{contacts} \sim \mathrm{NegBin(\mu, k)}\)
| Model | Δ DIC |
|---|---|
| Collective | 0 |
| Individual | -5k |
| Covariate | -50k |
| Covariate individual | -52k |
Conversational contacts
Physical contacts
Symptoms
Influenza-like illness
\(\mathrm{ili} \sim \mathrm{Binomial(1, p)}\)
| Model | Δ DIC |
|---|---|
| Collective | 0 |
| Collective + contacts | +4 |
| Individual | +3k |
| Covariate | -21 |
| Covariate individual | -42 |
ILI covariate model
\(\mathrm{ili} \sim \mathrm{Binomial(1, p)}\)
\(\mathrm{logit}(p) = \alpha + \beta_\mathrm{a} \cdot \mathrm{age} + \ldots\)
ILI
Long-term collective dynamics in contact behaviour
Age of infection of chickenpox in the UK
Hypotheses
- Demographic change
- Change in social mixing
- Change in overall transmissibility
An age-structured model for long-term chickenpox dynamics
\(\beta_{ij}(t)\) varying stochastically, estimated as part of inference.
Summary & outlook
Summary
- People are different in the amount of contact they make
- Number of contacts appears unrelated to risk of acquiring ILI
- Long-term changes in contact rates can be estimated by combining disease & demographic data
Acknowledgements
Ken Eames, John Edmunds
The Flusurvey and Influenzanet teams and participants
